Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments

Gregor Steiner, Jeremie Houssineau, Mark Steel
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6537-6553, 2026.

Abstract

Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-steiner26a, title = {Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments}, author = {Steiner, Gregor and Houssineau, Jeremie and Steel, Mark}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6537--6553}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/steiner26a/steiner26a.pdf}, url = {https://proceedings.mlr.press/v337/steiner26a.html}, abstract = {Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.} }
Endnote
%0 Conference Paper %T Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments %A Gregor Steiner %A Jeremie Houssineau %A Mark Steel %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-steiner26a %I PMLR %P 6537--6553 %U https://proceedings.mlr.press/v337/steiner26a.html %V 337 %X Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.
APA
Steiner, G., Houssineau, J. & Steel, M.. (2026). Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6537-6553 Available from https://proceedings.mlr.press/v337/steiner26a.html.

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